Differential Quadrature Method for Stability and Sensitivity Analysis of Neutral Delay Differential Systems

This work develops a computationally efficient stability analysis method for the neutral delay differential systems. This method can be also conveniently applied for the optimal parameter tuning of related control systems. To facilitate this development, at each sampling grid point, the time derivative of the concerned differential system is first estimated by the differential quadrature method (DQM). The neutral delay differential system is then discretized as numbers of algebraic equations in the concerned duration. By combining the obtained discretized algebraic equations, the transition matrix of the two adjacent delay time durations can be explicitly established. Subsequently, the stability boundary is estimated, and the optimal parameters for the controller design are evaluated by searching the global minimum of the spectral radius of the transition matrix. In order to solve such optimization problems with the gradient descent algorithms, this work also analytically formulates the gradient of spectral radius of transition matrix with respect to the concerned parameters. In addition, a strong stability criterion is introduced to ensure better robustness. Finally, the proposed method is extensively verified by numeric examples, and the proposed differential quadrature method demonstrates good accuracy in both parameter tuning and stability region estimation for the neutral delay differential systems.